量子相对信息熵及其半正定优化  

Quantum Relative Entropy and Its Semi-Definition Optimization

作　　者：沈洁 

机构地区：[1]中国电力科学研究院有限公司信息通信研究所,北京100192

出　　处：《电力信息与通信技术》2017年第12期1-5,共5页Electric Power Information and Communication Technology

摘　　要：在多用户通信条件下,采用相对信息熵来计算信道容量。量子通信的多光子纠缠态,也可以借用量子相对熵对容量进行计算。文章对量子相对熵的定义、方程和性质进行了讨论;在量子纠缠态下,给出了通过量子相对熵计算信道容量的公式,并采用半正定规划法计算了纠缠辅助信道、退相干信道的容量;针对实时连续情况,讨论了相对熵与参考移动相对Fisher信息之间的关系;通过用热方程应用积分来计算导数,得出相对熵的积分表示;通过理论分析给出了相互信息量和相对熵的不等式,并仿真验证了两者之间的关系。文章研究得出以下结论:对于纠缠态和退相干条件下,互信息熵始终大于相对熵,不等式成立;纠缠态下信道容量能达到2,高于阻尼受限信道容量,从而可以在量子通信中采用半正定规划方法计算信道容量。In the multi-user communication conditions, the adaptation of relative information entropy is used to calculate the channel capacity. Quantum communication of the multi-photon entangled state, can also use the quantum relative entropy to calculate the capacity. In this paper, the definition, equation and properties of quantum relative entropy are discussed, the formula for the channel capacity in quantum entangled state is presented, and the semi-definite programming method is used to calculate the capacity of entangled auxiliary channel and decoherence channel. The relationship between the relative entropy and the reference mobile relative Fisher information is discussed. The derivative by applying the integral of the thermal equation is calculated to obtain the integral representation of the relative entropy. Through the theoretical analysis, the inequality of mutual information and relative entropy is given, and the simulation proves the relationship. The conclusion is that for the entangled and decoherence conditions, the mutual entropy is always greater than the relative entropy, and the inequality holds. Under the entangled state, the channel capacity can reach 2, which is higher than the damping limited channel capacity. The result can be used in quantum communication to calculate the channel capacity by semi-definite programming method.

关 键 词：量子相对熵 互信息量 FISHER信息量 半正定规划 量子纠缠 退相干信道 

分 类 号：TN918.91[电子电信—通信与信息系统]